How do I find the natural frequency?

There are a number of ways to find the natural frequency (resonance) of a part like an automotive inlet manifold. Here are three different types of popular test techniques. But which one should you use and why?

1. Response Analysis

The most straightforward solution is to simply attach an accelerometer (keeping in mind any temperature restrictions) to the part in question. Then run the engine at a steady speed and view an FFT spectrum of the of the vibration.

There are a number of issues with this technique. Most importantly, there is no way to separate which vibrations are resonances of the part of interest and which are caused by resonances of other parts, such as the block or head. Also, there will be a significant content caused by the running of the engine itself. All these sources will be mixed together and impossible to separate. For these reasons, this technique is not recommended. So how could the structural resonances and the vibrations caused by running the engine be separated?

2. Rotational Speed Analysis

First, we attach an accelerometer to the inlet manifold (with the part fitted to the engine) and then measure the engine crankshaft speed using a tachometer sensor. Then we measure both the vibration levels and shaft speed of the crankshaft while we vary the speed of the engine. Using this data we can create a waterfall plot. This plot will show us frequencies associated with the running of the engine. These include the various rotating parts and the ignition phase of the combustion process. More importantly for our test this waterfall will also show the structural resonances.

Although this technique will allow an engineer to find the natural frequency and vibrations caused by the engine running, it will not allow the separation of the natural resonances of the inlet manifold from the natural frequencies of the other parts of the engine. For that, another technique is required.

3. Hammer Impact Analysis

The most common and generally the most successful test for this sort of project is the Hammer Impact Test. This is often (incorrectly) called Modal Analysis or a Modal Test. See the article What Is Hammer Impact Testing? for more information.

A Hammer Test consists of attaching an accelerometer to a location on the structure or component. In our case this would be the inlet manifold. Importantly the manifold should not be attached to anything. In an idea world it would be in a totally free-free state, floating in space. In practice we suspend the test piece. With the accelerometer fixed in one position we then impact the force instrumented hammer in another position. For example, we might choose to fit the accelerometer at one end of the inlet manifold and impact the hammer at the other.

The hammer has a force sensor fitted to the head. The data acquisition system can then measure the excitation force from the hammer and measure the response acceleration from the accelerometer. Using this information a transfer function is calculated between these two points. We can then see how an excitation will cause certain frequencies to be excited in the structure. The transfer function will show the natural frequencies of the structure. The more complex the structure the more complex the transfer function.

Importantly, the engineer can clearly visualise the natural response of only the part in question.

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James Wren

Former Sales & Marketing Manager at Prosig

James Wren was Sales & Marketing Manager for Prosig Ltd until 2019. James graduated from Portsmouth University in 2001, with a Masters degree in Electronic Engineering. He is a Chartered Engineer and a registered Eur Ing. He has been involved with motorsport from a very early age with a special interest in data acquisition. James is a founder member of the Dalmeny Racing team.